Basic theorems in algebraic K-theory: Difference between revisions

Revision as of 01:46, 29 October 2019

Revision as of 05:26, 29 October 2019

Line 10:

The localization theorem generalizes the [[localization theorem for an abelian categories]].

{{math_theorem|name=Waldhausen Localization Theorem<ref>{{harvnb|Weibel|loc=Ch. V, Waldhausen Localization Theorem 2.1.}} </ref>|Let <math>A</math> be the category with cofibrations, equipped with two categories of weak equivalences, <math>v(A) \subset w(A)</math>, such that <math>(A, v)</math> and <math>(A, w)</math> are both Waldhausen categories. Assume <math>(A, w)</math> has a [[cylinder functor]] satisfying the Cylinder Axiom, and that <math>w(A)</math> satisfies the Saturation and Extension Axioms. Then

:<math>K(A^w) \to K(A, v) \to K(A, w)</math>

is a [[homotopy fibration]].

Line 39:

*GABE ANGELINI-KNOLL, [http://www.math.wayne.edu/~gak/talks/FTKthytalk.pdf FUNDAMENTAL THEOREMS OF ALGEBRAIC K-THEORY]

*Tom Harris, [https://arxiv.org/abs/1311.5162 Algebraic proofs of some fundamental theorems in algebraic K-theory]

{{algebra-stub}}

{{Uncategorized stub|date=October 2019}}